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图1(a)左右两幅图,分别为反射型超原子和透射型超原子。当正入射的圆偏振光照射到绕中心对称轴旋转角度ϕ的超原子上时,反射光束或者透射光束中手性与入射光相反的圆偏振光获得的相位延迟为
$ \pm 2\phi $ 。以透射型超表面为例,其透射特性可以用Jones矩阵来描述[19-20]:图 1 (a)反射型和透射型超表面的几何相位调控机理 [19-20];(b)共振相位型超构表面设计原理[21];(c)基于波导传输相位的高对比度介质超表面HCMs (high-contrast metasurfaces)设计[23];(d)利用超构原子在单元周期内的相对位移实现迂回相位的超构表面设计[24]
Figure 1. (a) Geometric phase control mechanism for reflective and transmissive metasurfaces [19-20]; (b) Design principle of resonant phase metasurface [21]; (c) Design of high-contrast metasurfaces (HCMs) based on waveguide transmission phase [21]; (d) Utilizing the relative displacement of the meta-atoms in the unit period to realize the detour phase effect and the design of the metasurface[24]
$$ T=\left(\begin{array}{cc}{t}_{xx}& {t}_{xy}\\ {t}_{yx}& {t}_{yy}\end{array}\right)= R\left(-\phi \right)\left[\begin{array}{cc}{{A}_{x}{\rm{e}}}^{i{\varPhi }^{x}}& 0\\ 0& {A}_{y}{{\rm{e}}}^{i{\varPhi }^{y}}\end{array}\right]R\left(\phi \right) $$ (1) 式中:x,y分别为将超原子看作双折射晶体时的光学主轴(o轴或e轴);
${{A}_{x}{\rm{e}}}^{i\varPhi ^{x}}$ 和${A}_{y}{{\rm{e}}}^{i\varPhi ^{y}}$ 为响应的透射复振幅。当归一化入射的圆偏振光束:$$ {\widehat{{\rm{e}}}}_{\pm }\left(0\right)=\frac{1}{\sqrt{2}}\left({\widehat{{\rm{e}}}}_{x}\pm i{\widehat{{\rm{e}}}}_{y}\right) $$ (2) 沿z轴照射到周期性超原子阵列时,透射型周期性几何相超原子阵列的表征可以表示为:
$$ \begin{split}{E}_{\pm }^{t}=&T{\widehat{{\rm{e}}}}_{\pm }\left(0\right)=\frac{1}{2}\left({t}_{xx}+{t}_{yy}\right){\widehat{{\rm{e}}}}_{\pm }\left(0\right)+\\ &\frac{1}{2}\left({t}_{xx}-{t}_{yy}\right){{\rm{e}}}^{\pm i2\phi }{\widehat{{\rm{e}}}}_{\mp }\left(0\right) \end{split}$$ (3) 上式表明,输出场包含两个正交的圆偏振分量。第一个透射分量具有与入射光相同的偏振态,也称为共极化分量(co-polarized component)。第二项具有与入射光场相反的手性,称为交叉极化分量(cross-polarized component)。一般情况下近似地有Ax=Ay=A0,令δ= Φx−Φy, Φ0=(Φx+Φy)/2,进一步可以得到:
$$ {E}_{\pm }^{t}=\frac{{{A}_{0}{\rm{e}}}^{i\varPhi 0}}{2}{\rm{cos}}\frac{\delta }{2}{\widehat{{\rm{e}}}}_{\pm }\left(0\right)+i\frac{{{A}_{0}{\rm{e}}}^{i\varPhi 0}}{2}{\rm{sin}}\frac{\delta }{2}{{\rm{e}}}^{\pm i2\phi }{\widehat{{\rm{e}}}}_{\mp }\left(0\right) $$ (4) 由公式(4)可以看出,通过调整超构单元的几何尺寸,调整透射振幅和超原子传输相位延迟及面内旋转角可以改变两个分量的占比。当δ=(2n+1)π(n为任意整数) 时,即超原子为一半波片时,透射场只存在交叉分量并且具有2ϕ相位变化(即几何相位)。更进一步对传输相位和几何相位的联合调控可以实现左旋分量与右旋分量的振幅和相位的同时独立调控。
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图1(b)利用共振相位超表面实现了光束异常反射,通过改变H型天线结构的几何尺寸,实现了覆盖0~2π的超构原子设计[21]。另外共振相位的典型代表是惠更斯超表面 [22]。惠更斯超构原子是同时激发电偶极和磁偶极共振,能够同时实现对人工电磁表面面电流与磁流的调控。通过调整超原子几何构型,使其满足惠更斯条件:激发具有重叠的电共振与磁共振模式,从而实现更高的控制效率与更薄的单元厚度。如图1(c)所示,加州理工的Faraon教授研究团队提出了高对比度超表面,通过调整柱状纳米结构的横截面几何,实现了传输相位的连续变化调控[23]。其原理是纳米柱可以近似看为截断波导,通过调整共振波导模式的有效折射率来实现相位的连续可调。传输相位可以表达为Ψ=k0neffH,k0是自由空间波数,H为纳米柱的高度,neff是波导模式的有效折射率。这类超表面结构通常是将折射率较大的介质材料(Si, TiO2, GaN, 等)生长在折射率较低的衬底(SiO2, Al2O3等)上,所以也称为高对比度介质超表面(high-contrast metasurfaces,HCMs)。最近,研究人员基于迂回相位,将超构原子排列成光栅结构(如图1(d)所示),通过对表面等离激元共振间隙模式的精心调控,使得−1衍射级次上具有接近100%的衍射效率。迂回相位可以表示为
$ \varphi =\dfrac{2\pi p}{{p}_{0}} $ ,p是超构原子的相对位移,p0是超构单元周期[24]。通过丰富的相位调控机制尽可能地开发超构单元的独立自由度参数,组合多种相位调控方式,对光场各维度进行同时独立调控,是超表面光场调控物理研究发展的必然趋势,这在宽带消色差透镜的研究中表现尤为明显。 -
基于等光程原理,要使来自超表面不同位置的光线在设定的焦点位置汇聚,平面超构透镜上所需补偿的相位分布满足[25]:
$$ \varPhi \left(x,y\right)=-\frac{2\pi }{\lambda }\left(\sqrt{{x}^{2}+{y}^{2}+{F}^{2}}-F\right) $$ (5) 式中:F为焦距;λ为入射光波长;(x, y)为超表面上的空间坐标。通过在第1节所讨论的相位调控机制去进行超构原子的设计及优化,最后按照公式 (5) 进行排布,即可实现超构透镜的设计。此过程即通过在超表面上引入相位突变,将传统光学中的球面透镜聚焦转化为了平面透镜聚焦。如图2所示,总结了近年来超构透镜在提高透镜数值孔径和聚焦效率上的研究进展。图2(a)通过构造非对称超分子,通过超构原子之间的共振效应尽可能将光束散射到特定的大的偏折角度(约82°)上,实现了数值孔径(NA)接近1的薄的(λ/3)透射式超构透镜[26]。在参考文献[13]中,通过优化介质纳米柱结构的三个自由度参数:长度、宽度以及面内旋转角,基于几何相位超表面的设计,具有高数值孔径 (NA=0.82)和高聚焦效率(81%)的可见波长(λ=532 nm)超构透镜被研究报道,其性能可与最先进的商用物镜比拟。图2(b)为利用几何相位和光栅结构超构原子设计而成的具有70%聚焦效率的透射式介质超构透镜[27]。由于几何相位是与波长无关的,因此该几何相位超构透镜具有一定的宽带聚焦功能,但由于材料本征色散和单一波长的设计,焦距将随波长发生变化,存在一定的色差。同时,几何相位超构透镜工作在特定的圆偏振态。图2(c)展示了工作于近红外波长λ=1550 nm的偏振不敏感超构透镜,该超构透镜基于HCMs的波导传输相位实现聚焦相位分布[28]。HCMs超单元之间的相互耦合非常微弱,周期性超原子阵列的透射性能可以用单个超原子单元的透射矩阵来表征。在优化的单元周期下,光与周期性超原子阵列相互作用的近场能量几乎完全局域在单个纳米柱内。通过选择最优化的晶格常数,在一定的直径范围内,可以实现近100%的透射效率和连续的的全相位0~2π调控(如图1(c)所示)。并且该工作研究了不同数值孔径于聚焦效率的关系,高NA总是对应较低的聚焦效率。图2(d)和图2(e)报道了最近中波红外超构透镜的研究工作,图2(d)是基于偏振不敏感HCMs实现的具有高效聚焦和大NA的超构透镜[29],并且制作的超构透镜成像性能与相同指标的商用物镜相媲美。基于惠更斯超表面,图2(e)报道了一种超薄的(λ/8)中红外波长(λ=5200 nm)超构透镜,并且也实现了比拟商用物镜的成像效果[30]。
图 2 (a)基于非对称超构原子的超高数值孔径(NA>0.99)超构透镜[26];(b)基于几何相位的透射型超构透镜 [27];(c)基于HCMs超表面平台的近红外波长偏振不敏感超构透镜[28];(d) 基于Si/MgF2超表面平台的中波红外偏振不敏感超构透镜[29];(e)基于惠更斯超构表面的线偏振中红外波长超薄超构透镜[30]
Figure 2. (a) Ultra-high numerical aperture (NA>0.99) meta-lens based on asymmetric metaatoms[26]; (b) Transmissive metalens based on geometric phase[27]; (c) Near-infrared wavelength polarization-insensitive metalens based on HCMs meta-surface platform[28]; (d) Mid-wavelength infrared polarization-insensitive metalens based on the Si/MgF2 metasurface platform[28]; (e) Linearly polarized mid-infrared wavelength ultra-thin metalens based on Huygens metasurface[30]
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尽管超构透镜在设计的最优波长下具有精确的相位调控能力,超构透镜的性能已经可以达到与商用器件媲美的程度,但是缺乏对相位色散的修正及其他维度的调控能力。在实际的应用过程中仍然会遭受系统色差的限制,导致其成像性能的下降。因此修正超构表面器件的色差是一项十分具有挑战性和令人感兴趣的研究课题,因为具有宽带消色差能力的超表面器件由于具有超薄的平面构型和CMOS兼容的加工制造工艺将革新传统的光学系统,带来光学研究的重大进步。振奋人心的是,目前国际上各个研究团队已经报道并实现了宽带消色差超构透镜,并初步建立了具有一般性的消色差超构光学理论。以上基于单一型相位调控机制的超表面一般仅能对所调控光场的某一个维度(相位、相位色散、偏振态)进行单独调控。为了实现宽波段无消色差超构透镜,需要对空间光场的相位、色散等各个维度实施全方位自由调控。
图3(a)展示了利用表面等离激元集成共振相位与几何相位结合的调控方法实现了工作于近红外波段的反射式宽带消色差超构透镜。该工作提出了一般性的宽带消色差超构器件设计理论,通过几何相位在中心波长处引入实现聚焦功能的相位分布,同时借助超构原子的共振相位对相位色散所导致的群延迟相位进行调制,从而实现相位与相位色散的同时独立调控[31]。图3(b)基于这种相位和群延迟调控机制,在集成共振波导相位的基础上,利用GaN纳米柱超构原子及其互补结构,增大了群延迟相位的覆盖范围[32],开发出了工作于整个可见光波段的透射型宽带消色差超构透镜,并进行了白光成像实验展示。总的来说,这种宽带消色差机制一方面通过几何相位实现超构透镜聚焦所需满足的相位分布;另一方面通过超构原子的共振相位对光场传播所累积的色差进行修正。可以通过金属超分子的集成共振机理、高深宽比GaN纳米柱及其互补构型组合的超原子结构或者如图3(c)所示的双TiO2纳米柱超分子构型来实现相位与群延迟相位的同时独立调控[33]。
图 3 (a)基于集成等离激元共振相位和几何相位的反射式宽带消色差超构透镜[31];(b) GaN纳米柱集成共振相位的透射型宽带消色差超透镜及其消色差成像[32];(c) 基于TiO2超表面平台的的可见光透射型宽带消色差超透镜[33];(d)偏振不敏感宽带消色差超透镜阵列的白光3D成像展示[34];(e)工作在近红外波段的偏振不敏感消色差超透镜与无色差修正超透镜对比[35];(f) 可工作在可见至近红外波长(640~1200 nm)的超宽带消色差偏振不敏感超构透镜[36]
Figure 3. (a) Reflective broadband achromatic meta-lens based on integrated plasmon resonance phase and geometric phase [31]; (b) Transmissive broadband achromatic metalens via integrated resonance phase of GaN nanopillar and the achromatic imaging[32]; (c) Transmission broadband achromatic metalens in the visible band based on TiO2 metasurface platform [33]; (d) 3D imaging demonstration of white light based polarization-insensitive broadband achromatic metalens array [34]; (e) Comparison of polarization-insensitive achromatic metalens working in the near-infrared band and the metalens without correction of chromatic aberration[35]; (f) Ultra-broadband achromatic polarization-insensitive metalens that can work from visible to near infrared wavelength (640-1 200 nm)[36]
基于几何相位和共振相位组合的消色差超构透镜展现出了较好的白光成像效果,为超表面透镜的实用化进程奠定了坚实的基础。但同时也存在对入射光场偏振的依赖,另外该类复合型相位对波前信息的调控仍然是依赖超构单元面内转角自由度所产生的几何相位,因此这类消色差超构透镜的聚焦效率受到了超构原子的群延迟相位和偏振转化效率之间的制约关系限制,聚焦效率不高(20%~40%)。图3(d)~3(f)通过利用对称的超构原子,克服了以上消色差超构透镜的偏振依赖性和聚焦效率不高的难题。图3(d)利用消色差超构透镜阵列实现了可见光波段的三维白光成像[34]。利用共振波导效应,图3(e)通过设计大深宽比和多样化的超构原子实现了较大的相位色散覆盖范围和近红外波段(1 250~1 650 nm)的透射型消色差超构透镜[35]。图3(f) 基于以上相位和相位色散调控原理,通过数值优化算法实现了可见-近红外波长(600~1 200 nm)的偏振不敏感超宽带消色差聚焦,并且聚焦效率突破到70%[36]。
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以上关于消色差超构透镜的报道仅局限于可见和近红外波段,同时未有对偏振调控的多功能消色差超构透镜的相关研究。相比可见和近红外,中波红外超构光学由于昂贵的实验表征设备和匮乏的光学元件而很少被研究报道。然而作为大气窗口之一和分子振动吸收谱带,中波红外光学具有很多重要的应用价值,如分子指纹检测等。传统的光学是通过分立式的偏振片、棱镜和透镜级联的方法来进行系统色差修正和偏振分光调制的。笔者研究团队近期利用全硅双折射超表面体系在中波红外范围实现了偏振-色散调制多功能超构光学器件[18]。如图4(a)所示,在连续的设计带宽内,不同偏振态的光子经过超表面器件调制后将携带不同的轨道角动量信息,并被收集到设定的焦平面上。另外,通过在超表面器件的调制偏振-相位色散谱中引入离轴相位因子,对宽带光束实现了无色散的定向聚束调控。由于偏振态的联合操控,不同偏振态的光子也以高的偏振隔离度被收集汇聚到焦平面的不同设计区域(见图4(b))。该器件在中波红外3.5~5 μm的连续带宽内可选择性地将不同偏振态的光子以特定的波前形式聚焦到同一焦平面的不同位置。实现结果表明,聚焦光斑具有接近衍射极限的尺寸和高偏振选择比(图4(c)~4(d))。该研究成果有望在机器视觉以及分子检测等领域得到应用。
图 4 (a)多功能硅基超构表面的偏振调控宽带消色差聚焦涡旋光束产生示意图;(b)不同偏振态下光斑中心横向位移随波长的变化曲线;(c)测量的偏振消光比;(d)光斑的半高宽和衍射极限表征
Figure 4. (a) Schematic diagram of polarization-controlled broadband achromatic focused vortex beam generation on a multifunctional silicon-based metasurface; (b) Curve of the lateral displacement of the spot center with wavelength in different polarization states; (c) Measured polarization extinction ratio; (d) Characterization of the FWHMs and diffraction limits of the spots
Research progress of broadband achromatic infrared metalens (Invited)
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摘要: 超构透镜是由亚波长散射单元结构排列而成的具有聚焦功能的平面二维超构表面。超构表面能够在亚波长尺度上操控光场的振幅、相位、色散和偏振态,是近年来迅速发展起来的新型光场调控载体。亚波长共振纳米结构使得高阶衍射被抑制,入射光场可以完美地被调制到设计的衍射级次上,从而确保了超构表面器件具有高的光子调控效率。同时,超构单元在设计上的灵活性及其特定的电磁响应使得超构表面可以实现对光场多个维度的定制化操控。不同于传统光学透镜依赖光传播的相位累积效应,宽带消色差超构透镜通过对光场相位和相位色散的同时独立调控解决了传统通过级联多个透镜修正色差造成的光学系统复杂和体积庞大限制,为发展小型化片上集成光学提供了全新的思路。文中围绕超构透镜的相关研究,首先介绍了超构表面调控光场振幅、相位和偏振态的基本原理,在此基础上,重点回顾了近年来关于超透镜的研究发展,包括通过单一参量调控的单波长超透镜的实现,以及通过对光场偏振、相位及相位色散的多参量联合调控的多功能宽带消色差超构透镜的发展现状,最后讨论其进一步发展的可能挑战与应用前景。Abstract: Metalenses are two-dimensional metasurfaces composed of sub-wavelength scatters with planar configuration and light focusing function. They can manipulate the amplitude, phase, dispersion and polarization of the light field at sub-wavelength spatial resolution, and develop rapidly in recent years. The subwavelength resonant nanostructure suppresses the high-order diffraction, and the incident light can be perfectly modulated to the predesigned diffraction order, thus ensuring the high efficiency of the metadevice for manipulating the photons. Besides, the design flexibility and specific electromagnetic response of the meta-unit enable metasurfaces to achieve customized control of the multiple dimensions of the light field. In contrast to the traditional refraction lens relying on the phase accumulation effect, the broadband achromatic metalens resolves the complex and bulky limitations of the traditional optical system caused by cascading multiple lenses to correct the chromatic aberration by independently and simultaneously manipulating the phase and phase dispersion of the optical field. It provides a promising way for the miniaturization of on-chip integrated photonics. Focusing on the progress of metalens, this review discussed the basic principles of metasurface on engineering the amplitude, phase and polarization state of the light firstly. Then the development of metalens in recent years was focused on, including the realization of single-wavelength metalens and the development of multi-functional broadband achromatic metalenses through manipulating the multiple parameters (polarization, phase and phase dispersion). Finally, the potential challenges and application prospects for further developing the metalenses were discussed.
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Key words:
- metalens /
- phase dispersion /
- achromatic imaging /
- polarization control
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图 1 (a)反射型和透射型超表面的几何相位调控机理 [19-20];(b)共振相位型超构表面设计原理[21];(c)基于波导传输相位的高对比度介质超表面HCMs (high-contrast metasurfaces)设计[23];(d)利用超构原子在单元周期内的相对位移实现迂回相位的超构表面设计[24]
Figure 1. (a) Geometric phase control mechanism for reflective and transmissive metasurfaces [19-20]; (b) Design principle of resonant phase metasurface [21]; (c) Design of high-contrast metasurfaces (HCMs) based on waveguide transmission phase [21]; (d) Utilizing the relative displacement of the meta-atoms in the unit period to realize the detour phase effect and the design of the metasurface[24]
图 2 (a)基于非对称超构原子的超高数值孔径(NA>0.99)超构透镜[26];(b)基于几何相位的透射型超构透镜 [27];(c)基于HCMs超表面平台的近红外波长偏振不敏感超构透镜[28];(d) 基于Si/MgF2超表面平台的中波红外偏振不敏感超构透镜[29];(e)基于惠更斯超构表面的线偏振中红外波长超薄超构透镜[30]
Figure 2. (a) Ultra-high numerical aperture (NA>0.99) meta-lens based on asymmetric metaatoms[26]; (b) Transmissive metalens based on geometric phase[27]; (c) Near-infrared wavelength polarization-insensitive metalens based on HCMs meta-surface platform[28]; (d) Mid-wavelength infrared polarization-insensitive metalens based on the Si/MgF2 metasurface platform[28]; (e) Linearly polarized mid-infrared wavelength ultra-thin metalens based on Huygens metasurface[30]
图 3 (a)基于集成等离激元共振相位和几何相位的反射式宽带消色差超构透镜[31];(b) GaN纳米柱集成共振相位的透射型宽带消色差超透镜及其消色差成像[32];(c) 基于TiO2超表面平台的的可见光透射型宽带消色差超透镜[33];(d)偏振不敏感宽带消色差超透镜阵列的白光3D成像展示[34];(e)工作在近红外波段的偏振不敏感消色差超透镜与无色差修正超透镜对比[35];(f) 可工作在可见至近红外波长(640~1200 nm)的超宽带消色差偏振不敏感超构透镜[36]
Figure 3. (a) Reflective broadband achromatic meta-lens based on integrated plasmon resonance phase and geometric phase [31]; (b) Transmissive broadband achromatic metalens via integrated resonance phase of GaN nanopillar and the achromatic imaging[32]; (c) Transmission broadband achromatic metalens in the visible band based on TiO2 metasurface platform [33]; (d) 3D imaging demonstration of white light based polarization-insensitive broadband achromatic metalens array [34]; (e) Comparison of polarization-insensitive achromatic metalens working in the near-infrared band and the metalens without correction of chromatic aberration[35]; (f) Ultra-broadband achromatic polarization-insensitive metalens that can work from visible to near infrared wavelength (640-1 200 nm)[36]
图 4 (a)多功能硅基超构表面的偏振调控宽带消色差聚焦涡旋光束产生示意图;(b)不同偏振态下光斑中心横向位移随波长的变化曲线;(c)测量的偏振消光比;(d)光斑的半高宽和衍射极限表征
Figure 4. (a) Schematic diagram of polarization-controlled broadband achromatic focused vortex beam generation on a multifunctional silicon-based metasurface; (b) Curve of the lateral displacement of the spot center with wavelength in different polarization states; (c) Measured polarization extinction ratio; (d) Characterization of the FWHMs and diffraction limits of the spots
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